We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example we build lattice fractons in odd $D$ spatial dimensions and their $(D+1)$ effective theory. The model possesses an anti-symmetric $K$ matrix resembling that of hierarchical quantum Hall states. The gauge charges are conserved in sub-dimensional manifolds which ensures the fractonic behavior. The construction extends to any lattice fracton model built from commuting projectors and with tensor products of spin-$1/2$ degrees of freedom at the sites.
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- Boston University [BU]
- Conselho Nacional de Desenvolvimento Científico e Tecnológico / National Council for Scientific and Technological Development [CNPq]
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (through Organization: Coordenação de Aperfeicoamento de Pessoal de Nível Superior [CAPES])
- United States Department of Energy [DOE]